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Thermodynamic curvature from the critical point to the triple point

I evaluate the thermodynamic curvature $R$ for fourteen pure fluids along their liquid-vapor coexistence curves, from the critical point to the triple point, using thermodynamic input from the NIST Chemistry WebBook. In this broad overview, $R$ is evaluated in both the coexisting liquid and vapor phases. $R$ is an invariant whose magnitude $|R|$ is a measure of the size of mesoscopic organized structures in a fluid, and whose sign specifies whether intermolecular interactions are effectively attractive ($R<0$) or repulsive ($R>0$). I discuss five principles for $R$ in pure fluids: 1) near the critical point, the attractive part of the interactions forms loose structures of size $|R|$ proportional to the correlation volume $ξ^3$, and sign of $R$ negative, 2) in the vapor phase, there are instances of compact clusters of size $|R|$ formed by the attractive part of the interactions and prevented from collapse by the repulsive part of the interactions, and sign of $R$ positive, 3) in the asymptotic critical point regime, the $R$'s in the coexisting liquid and vapor phases are equal to each other, i.e., commensurate, 4) outside the asymptotic critical point regime incommensurate $R$'s may be associated with metastability, and 5) the compact liquid phase has $|R|$ on the order of the volume of a molecule, with sign of $R$ negative for a liquidlike state held together by attractive interactions and sign of $R$ positive for a solidlike state held up by repulsive interactions. These considerations amplify and extend the application of thermodynamic curvature in pure fluids.